ARJUN PRAKASH · RESEARCH SYSTEM ONLINE 00:00:00 UTC

INTELLIGENCE IN MOTION

I’m Arjun Prakash. I research reinforcement learning, multi-agent systems, optimization, and adaptive intelligence—and build interactive experiments that make the mathematics visible.

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01THESIS

The interesting problems live between worlds.

Between continuous dynamics and discrete decisions. Between simulation and reality. Between what a system predicts and what the world permits.

This space is a notebook for making those boundaries visible—and then moving them.

02RESEARCH 01 · SPECTRAL COLLAPSE
PAPER 01 SEP · 2025 ARXIV:2509.22335
CONTINUAL LEARNING · CURVATURE

Spectral Collapse Drives Loss of Plasticity in Deep Continual Learning

Arjun Prakash · Naicheng He · Kaicheng Guo · Saket Tiwari · Ruo Yu Tao · Tyrone Serapio · Amy Greenwald · George Konidaris

VISUALIZED CLAIM

As meaningful curvature directions disappear, a network loses the degrees of freedom it needs to learn the next task.

READ ABSTRACT

Deep networks can progressively lose plasticity in continual learning, becoming unable to fit new tasks without reinitialization. We identify Hessian spectral collapse at new-task initialization as a precursor to this failure: useful curvature directions vanish and gradient descent becomes ineffective. Rank-based trainability conditions connect this behavior to the loss-weighted Gram matrix and generalized Gauss–Newton curvature, motivating feature-rank preservation and L2 regularization to keep networks adaptable.

3D SPACE · RANK 64 4,096 PARTICLES · WEBGL2
X · Y · Z FREE

A deliberately stylized metaphor for dimensionality—not a numerical reconstruction. The same 4,096 particles keep moving, but each collapse removes a direction permanently until the sequence is reset.

03RESEARCH 02 · BILEVEL POLICY OPTIMIZATION
PAPER 02 MAY · 2025 ARXIV:2505.11714
REINFORCEMENT LEARNING · BILEVEL OPTIMIZATION

Bi-Level Policy Optimization with Nyström Hypergradients

Arjun Prakash · Naicheng He · Denizalp Goktas · Jacob Makar-Limanov · Amy Greenwald

VISUALIZED CLAIM

Figure 1, rendered live: four update rules carry the same initial states toward cycles, delay, or a Stackelberg equilibrium.

LIVE EULER INTEGRATION
READ ABSTRACT

Actor–critic reinforcement learning is naturally a bilevel problem because the actor depends on a critic that is itself learning a best response. BLPO nests critic updates and gives the actor a hypergradient that accounts for how the critic changes. A Nyström approximation makes the required inverse-Hessian computation more stable, while the theory establishes convergence to local strong Stackelberg equilibria under a linear critic parameterization and experiments show competitive control performance.

SIMULATING 630,000 STATES
STEP SIZEα = 0.05
REGULARIZERλ = 0.3
INITIAL STATES5 × 5 GRID
DOMAIN[−1, 1]²

Trajectories use the supplied update equations, clipping, and arc-length resampling. Every trajectory head is a metaball: cycling stretches the field apart while convergence fuses all 25 at equilibrium. A click now injects momentum at that phase-space coordinate; particle repulsion, boundary collisions, and damping physically produce the next 25 initializations, which are then shared across all four rules for a fair replay. In panels (c) and (d), the final 12 display samples ease to the equilibrium exactly as supplied.

04RESEARCH 03 · REACH–AVOID STACKELBERG GAME
PAPER 03 NEURIPS · 2023 ARXIV:2401.12437
MULTI-AGENT RL · GAME THEORY

Convex-Concave Zero-Sum Markov Stackelberg Games

Denizalp Goktas · Arjun Prakash · Amy Greenwald

VISUALIZED CLAIM

Two policies train inside the paper’s zero-sum reach–avoid experiment: one reaches the goal while the other learns to capture it.

READ ABSTRACT

Zero-sum Markov Stackelberg games model sequential decisions in continuous state and action spaces. We develop policy-gradient methods that learn from noisy trajectory estimates and converge in polynomial time for convex-concave games. Reach–avoid control arises naturally inside this framework: one player commits to a policy for reaching a target while the other learns a best response that blocks or captures it, with Stackelberg policies outperforming their Nash counterparts in the paper’s experiments.

INITIALIZING SELF-PLAY SHAPED · ALT 4:4 · 2 × REINFORCE 0 STEPS/S
REWARD SIGNAL
PROGRESS + SEPARATION + TERMINAL
UPDATE SCHEDULE
4 REACH BATCHES · 4 DEFEND BATCHES
UPDATE000
SELF-PLAY GAMES0000
REACH WINS · 50 AVG0%
CAPTURES · 50 AVG0%
OUTCOME TIMELINE · ALL SELF-PLAY GAMES · 12-GAME ROLLING RATE
DUBINS DYNAMICS · TOROIDAL WORLDpi ∈ 𝕋²  ·  ẋi = vi cos ψi  ·  ẏi = vi sin ψi  ·  ψ̇i = ωi
ZERO-SUM PAYOFFJdefend = −Jreach  ·  ‖pr − pd‖ ≤ rcap ⇒ loss

Both two-layer policies are trained from scratch in this tab with REINFORCE, running baselines, and Adam. Alternating mode uses four reach batches followed by four defender batches. Nested mode holds the defender fixed for eight reach-policy inner updates, then takes one defender outer update against the adapted reach policy. Shaped and sparse rewards remain exactly zero-sum. Every reward/schedule combination keeps independent weights, optimizer state, counters, and timeline while this tab is open. The toroidal mathematics still uses shortest wrapped geometry, but only one canonical copy of the world is rendered.

05RESEARCH 04 · STRUCTURAL CLUSTERING
PAPER 04 AMF · 2022 ARXIV:2004.09963
QUANTITATIVE FINANCE · CHANGE POINTS

Structural Clustering of Volatility Regimes for Dynamic Trading Strategies

Arjun Prakash · Nick James · Max Menzies · Gilad Francis

VISUALIZED CLAIM

A rank statistic detects volatility shifts online, turning one continuous stochastic path into structurally distinct regimes.

READ ABSTRACT

Nonstationary financial time series can be simplified into recurring volatility regimes without imposing a parametric switching model. The method first uses change-point detection to partition returns into locally stationary segments, compares the resulting distributions, and clusters them into a learned number of characteristic behaviors. Those historical regimes then support an online trading strategy that matches current market behavior to the past and dynamically manages risk.

CALIBRATING RANKS WIENER INCREMENTS · ONLINE MOOD CPM t = 000
MAX MOOD SCORE0.00σ
ESTIMATED BREAK—
DETECTION DELAY—
CONFIRMED SEGMENTS01
STOCHASTIC PROCESSdXt = σr(t)dWt
MOOD DISPERSION SCOREM′ = Σ(Ri − (N + 1)/2)²  ·  Z = |M′ − μ| / σM

This uses the paper’s rank-based statistic on every admissible split of the current run. When the maximum crosses the selected threshold, the estimated split is confirmed and the detector restarts there—so the bright detection pulse naturally arrives after the quieter, dashed change-point estimate. Confirmed segments are coloured by their realized RMS volatility σ̂: cyan below 0.78, violet from 0.78 to 1.55, and coral above 1.55. These are legibility thresholds, not the paper’s downstream Wasserstein/spectral clusters. The window then keeps sliding forever. The paper’s full CPM implementation calibrates time-varying thresholds to ARL0 = 10,000.

06METHOD

A loop, not
a pipeline.

Every useful system is an argument with reality.

  1. 01

    Frame the boundary.

    Name the actual system, its state, its constraints, and the thing that would count as progress.

  2. 02

    Build the smallest world.

    Create a model simple enough to interrogate and rich enough to fail in revealing ways.

  3. 03

    Instrument everything.

    Make behavior observable. A metric says what happened; an instrument helps explain why.

  4. 04

    Stress the assumptions.

    Move beyond the nominal case. Perturb, ablate, adversarially probe, and look for phase changes.

  5. 05

    Return to reality.

    Close the loop. Let evidence rewrite the model, the interface, and sometimes the question itself.

07LIVE SIGNAL

This page is
the instrument.

A procedural field, rendered on your device. No video. No stock imagery. Every frame is synthesized from time, movement, and position.

RENDERERDETECTING
COLOR SPACESRGB
FRAME RATE— FPS
MOTIONACTIVE
POINTER X/Y0.00 / 0.00
SCROLL DEPTH000%

WHAT IF THE INTERFACE
THOUGHT IN PUBLIC?

SPECIMEN A—26
END OF TRANSMISSIONBEGINNING OF SYSTEM

STAY CURIOUS.

Designed and computed at the edge.
One page. Zero frameworks. Infinite states.

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